Magnetic thermal switch for heat management at the nanoscale

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Magnetic thermal switch for heat management at the nanoscale

Riccardo Bosisio, Stefano Valentini, Francesco Mazza, Giuliano Benenti, Rosario Fazio, Vittorio Giovannetti, and Fabio Taddei

Phys. Rev. B 91, 205420 – Published 14 May 2015

Abstract

In a multiterminal setup, when time-reversal symmetry is broken by a magnetic field, the heat flows can be managed by designing a device with programmable Boolean behavior. We show that such a device can be used to implement operations, such as on/off switching, reversal, selected splitting, and swap of the heat currents. For each feature, the switching from one working condition to the other is obtained by inverting the magnetic field. This offers interesting opportunities for conceiving a programmable setup, whose operation is controlled by an external parameter (the magnetic field) without need to alter voltage and thermal biases applied to the system. Our results, generic within the framework of linear response, are illustrated by means of a three-terminal electronic interferometer model.

Received 1 April 2015
Revised 24 April 2015

DOI:https://doi.org/10.1103/PhysRevB.91.205420

Authors & Affiliations

Riccardo Bosisio^1,2,*, Stefano Valentini³, Francesco Mazza³, Giuliano Benenti^4,5, Rosario Fazio³, Vittorio Giovannetti³, and Fabio Taddei²

¹SPIN-CNR, Via Dodecaneso 33, 16146 Genova, Italy
²NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56126 Pisa, Italy
³NEST, Scuola Normale Superiore, Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
⁴Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy
⁵Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy

^*Corresponding author: riccardo.bosisio@nano.cnr.it

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Vol. 91, Iss. 20 — 15 May 2015

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Images

Figure 1
Examples of operational principles for a three-terminal magnetic thermal switch. The different panels illustrate the heat current (a) multiplier, (b) selector, (c) reversal, and (d) swap configurations, respectively. The working operation is selected by choosing either $+ B$ or $- B$ . Solid (dashed) lines correspond to $J^{Q} (+ B) [J^{Q} (- B)]$ , whereas black (red) lines refer to currents flowing from terminal 1(2). Notice that in panel (a) lines of different thicknesses have been used to emphasize the increase/decrease of the heat currents magnitude before and after the magnetic-field reversal.
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Figure 2
Sketch of the three-terminal magnetic thermal switch studied numerically: an electronic interferometer, pierced by a magnetic flux $Φ$ and in contact with three reservoirs at different temperatures $T_{k}$ and electrochemical potentials $μ_{k} (k = 1, 2, 3)$ . The scattering region $S_{s}$ inside channel 1 breaks the particle-hole symmetry. $L_{+}$ and $L_{-}$ are the interference paths and must be different in order to observe interference at the end of the device.
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Figure 3
Working operations of the three-terminal magnetic thermal switch discussed in the text. The heat currents through channels 1 (black squares) and 2 (red circles) are shown as a function of the magnetic flux $Φ$ enclosed in the interferometer. For completeness, the particle currents (black and red dashed lines) are also shown to emphasize that they do not follow the same behaviors as the heat currents. (a) Heat current multiplier: By reversing $Φ$ from $Φ_{0} = - π / 2$ to $- Φ_{0} = + π / 2, J_{1}^{Q}$ is halved whereas $J_{2}^{Q}$ is doubled. (b) Heat path selector: For $Φ_{0} = - π / 2, J_{1}^{Q}$ is finite whereas $J_{2}^{Q}$ is blocked. The situation is opposite by reversing $Φ$ to $- Φ_{0}$ . (c) Heat current reversal: By reversing $Φ$ from $- π / 2$ to $+ π / 2$ , the signs of both $J_{1}^{Q}$ and $J_{2}^{Q}$ flip. (d) Heat current swap: By reversing $Φ$ from $- 3 π / 4$ to $+ 3 π / 4$ , the values of $J_{1}^{Q}$ and $J_{2}^{Q}$ are interchanged. The parameters are $k_{B} T = 1, μ = 0, X_{1}^{T} = 0.025, X_{2}^{T} = 0.01$ [except in (c), where $X_{1}^{T} = - 0.005$ and $X_{2}^{T} = 0.005]$ and the difference between the interference paths in the upper/lower interferometer arms is $Δ (k L) \equiv k (L_{+} - L_{-}) = π / 2$ . Dotted blue lines are guides to the eye at $J^{Q} = 0$ , whereas gray lines highlight the magnetic flux values $Φ = \pm Φ_{0}$ selecting the two Boolean configurations.
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Figure 4
Sketch of the system used to model the interferometer discussed in Sec. 3. Two identical four-arm beam splitters are connected via two clean electronic waveguides of lengths $L_{+}$ and $L_{-}$ , forming an interference loop which is pierced by a magnetic flux $Φ$ . A scatterer $S_{s}$ is inserted into arm 1 in order to break the particle-hole symmetry. The numbers from 1 to 8 refer to the arms of the beam splitters and label the transmission and reflection amplitudes $t_{i j}$ and $r_{i j}$ (in particular, channel 4 is assumed to be totally reflective). The system is connected to three electronic reservoirs $R_{1}, R_{2}$ , and $R_{3}$ .
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